In vertical staff tachymetry, upper stadia reading = 0.1095 m, lower stadia reading = 0.0611 m, and the reference length S = 3 m. Calculate the horizontal distance.
Correct Answer: A. 62 m
📚 Detailed Explanation: Horizontal Distance from Vertical Staff Method = 62 m
Why A (62 m) is correct: In vertical staff tachymetry, the horizontal distance D is calculated as D = S / (difference in stadia intercepts at two positions). Here S = 3 m, upper stadia − lower stadia = 0.1095 − 0.0611 = 0.0484 m, giving D = 3/0.0484 ≈ 62 m.
Given:
Constant S = 3 m (staff interval or baseline)
Upper stadia reading at one position = 0.1095 m
Lower stadia reading = 0.0611 m
Constant S = 3 m (staff interval or baseline)
Upper stadia reading at one position = 0.1095 m
Lower stadia reading = 0.0611 m
Stadia intercept = Upper – Lower = 0.1095 – 0.0611 = 0.0484 m
Horizontal distance:
D = S / stadia intercept = 3 / 0.0484 = 61.98 m ≈ 62 m
Vertical Staff Tachymetry Principle
| Method | Formula | Notes |
|---|---|---|
| Standard stadia (anallatic) | D = 100 × S | S = upper stadia − lower stadia; simpler |
| Vertical staff distance measurement | D = L / (S1 − S2) | L = known reference distance; S1, S2 = stadia readings at two positions |
| This problem | D = 3 / (0.1095 − 0.0611) | D = 3 / 0.0484 = 62 m |
- D = 3 / (0.1095 − 0.0611) = 3 / 0.0484 = 62 m.
- The method uses the difference in stadia readings as the divisor.
- Larger stadia intercept difference → closer the staff; smaller difference → farther away.